Numerical Studies of Disk Formation Around Low-Mass Stars

While playing an essential role in star formation and planet formation, the origin of circumstellar disks remains a matter of debate. In particular, circumstellar disks are frequently observed in reality, yet magnetic fields in simulations readily suppress them. In synergies with astronomical observations, analytical and numerical calculations enable us to investigate the process of disk formation from prestellar cores to tens of thousands of years after the birth of the protostars. However, the diversity of the involved astrophysical processes and the wide ranges of length scales over eight orders of magnitude have hindered our attempts to simulate the formation of disks. In this thesis, we first approach the problem with idealized simulations that capture the essential physics. It is followed by using synthetic observation to understand the physics behind actual radio observations of protostars with embedded disks. Lastly, we describe the tools that are built for current and future investigations.

In the first project, we systematically investigate the roles of turbulence and ambipolar diffusion (AD) in the accretion phase of star formation using magnetohydrodynamic (MHD) simulations. We find that both turbulence and AD promote disk formation. In the turbulent simulations, rotationally supported disks form with and without AD. However, the disks formed without AD are strongly magnetized and short-lived. Turbulence also modifies the appearance of the magnetic field-induced pseudo-disks. The pseudo-disks are warped by turbulence while still staying coherent. In the simulations with AD, the magnetic flux is removed from the disks very efficiently, and the magnetic field lines are less pinched. It results in reduced magnetic braking and promotes disk formation. The disks formed with AD are highly unstable without turbulence. We conclude that turbulence and AD work in parallel to promote disk formation. We measure the plasma-β of the disks formed in our simulations. The disks are much more strongly magnetized than commonly assumed in the literature for driving protoplanetary disk accretion.

By comparing radio observations of protostars in the Perseus molecular cloud and the synthetic observations using the previous simulations, we explain the depolarization observed on the disk scale and the alignment of the polarization to the minor axes of the disks. A model is constructed by considering the Larmor precession time-scale, or the grain alignment time-scale, with the gas damping time scale to determine whether the grains are aligned. The vector radiative transfer equation is solved analytically and applied to the simulation to obtain a synthetic polarimetry observation. To reproduce the observed trends, we conclude that both grain dealignment and dust self-scattering must be present.

In the last part of the thesis, we describe three modules implemented in Athena++ to facilitate a range of current and future studies on star and disk formation. We implement the multipole expansion self-gravity solver to the code in spherical polar coordinates. Using the MacLaurin spheroid as a test, we find that the error converges as more terms in the multipole expansion are used. The error is less than 0.1% when a reasonable number of terms is included in the expansion. The general barotropic equation of state (EOS) and its applications are then discussed. A general form of the multi-power-law equation of state is derived and used to fit a realistic relationship between temperature and density obtained using complex radiation MHD simulation. Lastly, we describe an implementation of sink particles treatment. This treatment keeps some of the strengths while improving the weaknesses of an existing implementation of sink particles. These modules are used in various projects by collaborators, including astrochemistry of hot cores and first cores, centrifugal barriers in protostellar collapse, and grain growth in disk formation, some of which are briefly described in the thesis.